Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
814 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 219 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19145155 | C2 | semidirect |
| 3. #19134197 | C2 | semidirect |
| 4. #19134193 | C2 | semidirect |
| 5. #19134188 | C2 | semidirect |
| 6. #19134183 | C2 | semidirect |
| 7. C2×C8×C43⋊C8 | C2 | semidirect |
| 8. C43×#3160 | C2 | semidirect |
| 70. C2×C8×C43 | SD16 | semidirect |
| 109. C43⋊C8 | #135 | semidirect |
| 123. #3160 | D43 | semidirect |
| 156. C43 | #19596 | semidirect |
| 203. C2×C8 | #10621884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145155 | 2 |
| #19145023 | 2 |
| #19134197 | 2 |
| #19134193 | 2 |
| #19134188 | 2 |
| #19134183 | 2 |
| C2×C8×C43⋊C8 | 2 |
| C43×#3160 | 2 |
| #19596 | 43 |